Generalised conformal structure and its implications

We study the generalised conformal structure of the low-energy dynamics of D-branes in all dimensions and its implications on correlation functions. We begin by considering conformal symmetry and the way it acts on fields. Symmetries and the way they constrain correlation functions are discussed through the derivation of Ward identities. These are used in order to put constraints on CFT n-point functions. The low-energy dynamics of D-branes are discussed and an extensive proof of their generalised conformal symmetry is given. Next, we investigate the analogy of Ward identities for the generalised conformal structure and derive similar equations with an additional term which compensates for the transformation of the coupling constant. Such an equation is used to prove the constraints of generalised dilatations and later in order to study a specific example of this structure - the free massive boson. The thesis ends with a discussion on the implications of this study and possible future steps.